IEEE Communications Magazine • April 2002
59
signal to be received with delay spreads of up to
tens of microseconds [2]. For bit rates in the
range of tens of megabits per second, this trans-
lates to intersymbol interference that can span
up to 100 or more data symbols. For example, at
a 5 MHz symbol rate, a 20 ms multipath delay
profile spans 100 data symbols.
For channel responses spanning tens or hun-
dreds of symbols, practical modulation and anti-
multipath alternatives are:
• SC modulation with receiver equalization
done in the time domain
• OFDM
• SC modulation with receiver equalization in
the frequency domain
A brief description of each of these anti-mul-
tipath alternatives follows.
SINGLE-CARRIER MODULATION WITH
TIME DOMAIN EQUALIZATION AT THE RECEIVER
A conventional anti-multipath approach, which
was pioneered in voiceband telephone modems
and has been applied in many other digital com-
munications systems, is to transmit a single carri-
er, modulated by data using, for example,
quadrature amplitude modulation (QAM), and
to use an adaptive equalizer at the receiver to
compensate for intersymbol interference (ISI)
[3]. Its main components are one or more
transversal filters for which the number of adap-
tive tap coefficients is on the order of the num-
ber of data symbols spanned by the multipath.
For the above-mentioned 20 ms delay spread
example, this would mean a transversal filter
with at least 100 taps, and at least several hun-
dred multiplication operations per data symbol.
For tens of megasymbols per second and more
than about 30–50-symbol ISI, the complexity and
required digital processing speed become exorbi-
tant, and this time domain equalization approach
becomes unattractive.
OFDM
OFDM transmits multiple modulated subcarriers
in parallel [1]. Each occupies only a very narrow
bandwidth. Since the channel affects only the
amplitude and phase of each subcarrier, equaliz-
ing each subcarrier’s gain and phase does com-
pensation for frequency selective fading.
Generation of the multiple subcarriers is done
by performing inverse fast Fourier transform
(IFFT) processing at the transmitter on blocks
of M data symbols; extraction of the subcarriers
at the receiver is done by performing the fast
Fourier transform (FFT) operation on blocks of
M received samples. Typically, the FFT block
length M is at least 4–10 times longer than the
maximum impulse response span. One reason
for this is to minimize the fraction of overhead
due to the insertion of a cyclic prefix at the
beginning of each block. The cyclic prefix is a
repetition of the last data symbols in a block. Its
length in data symbols exceeds the maximum
expected delay spread. The cyclic prefix is dis-
carded at the receiver. Its purpose is to:
• Prevent contamination of a block by ISI
from the previous block
• Make the received block appear to be peri-
odic with period M
This produces the appearance of circular convo-
lution, which is essential to the proper function-
ing of the FFT operation.
Time domain equalization typically requires a
number of multiplications per symbol that is pro-
portional to the maximum channel impulse
response length. OFDM processing requires on
the order of log
2
M multiplications per data sym-
bol, counting both transmitter and receiver opera-
tions. Since M is proportional to the maximum
expected channel response length, OFDM
appears to offer a better performance/complexity
trade-off than conventional SC modulation with
time domain equalization for large (> about 20
taps) multipath spread [4]. A variation is adaptive
■ Figure 1. a) Power amplifier output power spectra [5] for a QPSK 256-point OFDM system: (a) spectrum with ideal power amplifier
(infinite power backoff); (b) spectrum with typical power amplifier with 10 dB power backoff; (c) FCC MMDS spectral mask; b) power
amplifier output power spectra [5] for a QPSK SC system: (a) spectrum with ideal power amplifier (infinite power backoff); (b) spec-
trum with typical power amplifier with 10 dB power backoff; (c) FCC MMDS spectral mask.